1. Field of the Invention
The present invention relates to a device for measuring film thickness in a non-destructive and contactless mode by an optical means, and more specifically to an optical film thickness measuring device which is capable of simultaneously measuring thickness of each layer of a two-layer optical film.
2. Description of the Prior Art
When spectral reflectance of an single-layer transparent optical film is measured with a spectral reflectance measuring device, pluralities of local maximum values and local minimum values appear with variation of wavelength .lambda. on a spectral reflectance curve due to the effect of interference between the reflected lights, and show periodical variations in conjunction with film thickness. When number of maximum points or minimum points existing between a wavelength .lambda..sub.a producing a local maximum or minimum value and another wavelength .lambda..sub.b producing another local maximum or minimum value is represented by N and refractive index is designated by n, it is known that thickness d of this film is given by the following formula: EQU d=(N/2n)[(.lambda..sub.b .multidot..lambda..sub.a)/(.lambda..sub.b -.lambda..sub.a)]
Most of the conventional optical film thickness measuring devices are based on this relationship.
When thickness of a multi-layer optical film is measured, however, a spectral reflectance curve is obtained as a total sum on which the periodicities of the spectral reflectance curves of the individual layers are overlapped with one another, thereby making it impossible to determine thickness of each layer simply by utilizing the formula mentioned above. For this reason, it was conventionally practised, for determining thickness of each layer of a multi layer film, to prepare a reference piece made of the same material as that of the substrate of the multi-layer film, form a layer on the reference piece as a single layer film which is same as the layer of the multi-layer film each time a layer is formed on the multi-layer film and determine thickness of each layer of the multi-layer film by measuring the single-layer film. However, this method posed important problems that it requires a very long time for completing measurements of thickness of all the layers and that it cannot always permit measuring thickness of each layer of the multi-layer film accurately since thickness of the individual layers laminated in the state of the multi-layer film is not necessarily the same as that of the layers measured in the state of the single layer films.
In order to solve these problems, the inventor et al proposed, as Japanese Preliminary Patent Publication No. 32307/63, an optical film thickness measuring device which is capable of simultaneously measuring thickness of the individual layers of a multi-layer film. This film thickness measuring device will be briefly described below taking measurement of thickness of a two-layer film as an example. This film thickness measuring device is based on a fundamental concept that thickness of the individual layers are to be determined so as to obtain a reflectance curve which is optimumly approximated to a spectral reflectance curve actually measured. Since refractive index is a function of wavelength, reflectance R of this two-layer film is given as a function of thickness, refractive index and wavelength as follows: EQU R=R{n.sub.1 (.lambda.), d.sub.1 ; n.sub.2 (.lambda.), d.sub.2 ; .lambda.}
wherein the reference symbols n.sub.1 and d.sub.1 represent refractive index and thickness respectively of a layer, and the reference symbols n.sub.2 and d.sub.2 designate refractive index and thickness of the other layer, and the reference symbol .lambda. denotes wavelength of the measuring light. When materials of the individual layers are known, n.sub.1 (.lambda.) and n.sub.2 (.lambda.) are constants at a definite wavelength, and reflectance R can be expressed as a function of the three variables: EQU R=R(d.sub.1, d.sub.2 ; .lambda.)
When reflectance values measured at wavelengths .lambda..sub.1, . . . , .lambda..sub.k are represented by R.sub.m (.lambda..sub.1), . . . , R.sub.m (.lambda..sub.k), thickness of the layers are determined as the solutions of simultaneous equations of a number of k: ##EQU1## Since strict solutions of the simultaneous equations are not always obtained in practice due to measuring errors and other conditions, thickness values of the two layers are determined as d.sub.1 and d.sub.2 which minimize total sum of differences between actually measured values and theoretical values at each wavelength. Accordingly, it is practised to set an evaluation function E such as: ##EQU2## and determine values of d.sub.1 and d.sub.2 so as to minimize value of the evaluation function. The global optimization method is adopted as a technique for this practice. This method can be outlined as follows. Since rough thickness values of the layers can be estimated from the manufacturing conditions, etc. of the film to be measured, ranges of d.sub.1 and d.sub.2 covering these values are specified as possible regions of solutions (when d.sub.1 is estimated as several hundred nanometers, for example, 100.ltoreq.d.sub.1 .ltoreq.1000 is specified as a possible region of the value of d.sub.1). Pairs of values of d.sub.1 and d.sub.2 of an adequately selected number p is sampled at random within these regions (i.e., values of d.sub.1 and d.sub.2 are optionally selected within these regions) and values of the evaluation functions E.sub.1, E.sub.2, . . . , E.sub.p corresponding these pairs are calculated by using these values of d.sub.1 and d.sub.2. This corresponds to evaluation of the difference between the spectral reflectance to be theoretically obtained from each pair of the two layers and the spectral reflectance of the two layers actually measured on an assumption of p pairs of the two layers having different thickness. It can therefore be said that the values of d.sub.1 and d.sub.2 which minimize the value of E (any one of E.sub.1, . . . , E.sub.p) are close to actual thickness values of the two layers. Then, within the possible region of solutions specified above, a narrower range is selected as a new possible region which includes such pairs of (d.sub.1 and d.sub.2) giving relatively small values of E, pairs of (d.sub.1 and d.sub.2) are sampled at random within this narrower region and values of the evaluation functions are calculated on the basis of these pairs. The possible region is narrowed step by step by repeating the procedures described above until a pair of (d.sub.1 and d.sub.2) giving the minimum value of E is obtained. Since this method allows to accurately determine the minimum value of the evaluation function E, it permits determining thickness of layers of a multi-layer films with high accuracy and is very preferable for practice.
However, this method requires repeating calculations of reflectance R(d.sub.1, d.sub.2 ; .lambda.) and the evaluation function E in the number cf sampled pairs of (d.sub.1 and d.sub.2), thereby posing a problem that it requires a long time from the measurement of spectral reflectance of a sample to determination of thickness of the individual layers. Especially in the recent years where objective lenses having relatively large numerical apertures are used for measuring spectral reflectance, the light for irradiating optical films includes the components in parallel with the optical axis and the components inclined at large angles with regard to the optical axis. For this reason, it is necessary for enhancing measuring accuracy to take considerations such as to use a mean value of reflectance of a plurality of light components having different angles of incidence as R(d.sub.1, d.sub.2 ; .lambda.) to be used for calculation of the evaluation function E, thereby further prolonging the time required for determination of layers of multi-layer film. Though it is possible to shorten the time required for measurement by selecting wider wavelength intervals so as to reduce number of k for .lambda..sub.1, . . . , .lambda..sub.k or decreasing the number of pairs of (d.sub.1 and d.sub.2) to be sampled, such a measure will mistake the means for the end since it will degrade measuring accuracy.